Tradeoffs between quantum and classical resources in linear combination of unitaries

Quantum Physics arXiv:2512.06260 (quant-ph) [Submitted on 6 Dec 2025] Title:Tradeoffs between quantum and classical resources in linear combination of unitaries Authors:Kaito Wada, Hiroyuki Harada, Yasunari Suzuki, Yuuki Tokunaga, Naoki Yamamoto, Suguru Endo View a PDF of the paper titled Tradeoffs between quantum and classical resources in linear combination of unitaries, by Kaito Wada and 5 other authors View PDF Abstract:The linear combination of unitaries (LCU) algorithm is a building block of many quantum algorithms. However, because LCU generally requires an ancillary system and complex controlled unitary operators, it is not regarded as a hardware-efficient routine. Recently, a randomized LCU implementation with many applications to early FTQC algorithms has been proposed that computes the same expectation values as the original LCU algorithm using a shallower quantum circuit with a single ancilla qubit, at the cost of a quadratically larger sampling overhead. In this work, we propose a quantum algorithm intermediate between the original and randomized LCU that manages the tradeoff between sampling cost and the circuit size. Our algorithm divides the set of unitary operators into several groups and then randomly samples LCU circuits from these groups to evaluate the target expectation value. Notably, we analytically prove an underlying monotonicity: larger group sizes entail smaller sampling overhead, by introducing a quantity called the reduction factor, which determines the sampling overhead across all grouping strategies. Our hybrid algorithm not only enables substantial reductions in circuit depth and ancilla-qubit usage while nearly maintaining the sampling overhead of LCU-based non-Hermitian dynamics simulators, but also achieves intermediate scaling between virtual and coherent quantum linear system solvers. It further provides a virtual ground-state preparation scheme that requires only a resettable single-ancilla qubit and asymptotically shows advantages in both virtual and coherent LCU methods. Finally, by viewing quantum error detection as an LCU process, our approach clarifies when conventional and virtual detection should be applied selectively, thereby balancing sampling and hardware overhead. Comments: Subjects: Quantum Physics (quant-ph) Cite as: arXiv:2512.06260 [quant-ph] (or arXiv:2512.06260v1 [quant-ph] for this version) https://doi.org/10.48550/arXiv.2512.06260 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kaito Wada [view email] [v1] Sat, 6 Dec 2025 03:10:22 UTC (264 KB) Full-text links: Access Paper: View a PDF of the paper titled Tradeoffs between quantum and classical resources in linear combination of unitaries, by Kaito Wada and 5 other authorsView PDFTeX Source view license Current browse context: quant-ph new | recent | 2025-12 References & Citations INSPIRE HEP NASA ADSGoogle Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) Links to Code Toggle Papers with Code (What is Papers with Code?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)